(CNN) -- The Supreme Court on Monday tried to make sense of conflicting standards when determining a key question in workplace discrimination claims: Who is the boss?

In an intense oral argument, the justices raised numerous scenarios to explore when a worker's actions were supervisory in nature but appeared uncertain on what approach was best for resolving the central legal question and whether a clear definition could even be established.

"There are situations where the assignment of [workplace] responsibilities is extremely unpleasant," said Justice Samuel Alito. "But there are also a lot of situations, where it's really very unclear. I don't know how courts are can grapple with that."

In a case closely watched by worker rights groups and business, a university catering employee claimed her work environment was a "living hell" due to the alleged actions of a fellow worker who she claimed was her supervisor even though the woman had no power to hire or fire her.

Maetta Vance was the only African-American in her office at Ball State University and had a long-running rift with white employee Saundra Davis. The matter included allegations of physical confrontations and racial epithets.

Vance filed various complaints with the Equal Employment Opportunity Commission and then sued in federal court, claiming her university kitchen was a "living hell."

The lawsuit argued Davis was a supervisor because she did not have to "clock in" and record her hours like other caterers and had authority in the kitchen to ensure daily tasks assigned by the chef and general manager -- her direct supervisors -- were performed.

But the university said it took corrective action to minimize personal conflicts between the two women, and that Davis did not have direct supervision over Vance and could not fire her.

Federal courts agreed with the university in Vance's case, using a narrow standard of defining a supervisor in dismissing the suit.

A gateway legal issue when first bringing allegations of discrimination or harassment is often figuring out whether the person instigating the wrongdoing is a "supervisor," and what authority that person has over the staff.

The high court has long said liability is automatically triggered when the boss harasses or threatens a subordinate.

If the conduct involves two co-workers with roughly the same duties, no legal action can be taken unless their manager was negligent in allowing the misconduct to continue.

Federal appeals courts are deeply divided over whether a "supervisor" is only someone with the power to "hire, fire, demote, promote, transfer, or discipline" employees as defined by the government; or more broadly, someone with the power to manage the day-to-day activities of colleagues.

During oral arguments, Chief Justice John Roberts wondered whether a senior employee who determined what music his co-workers heard on the job would make him a supervisor.

"That could be far more severe," said Roberts, "than, simply saying, you're going to-- as in this case-- be cutting the celery rather than baking the bread, or whatever."

Alito then jumped in. "What was the most unpleasant thing that Davis could have assigned [Vance] to do? Could it be chopping onions all day, every day?"

Vance's attorney Daniel Ortiz replied "chopping onions all day might be punishment" and could trigger a workplace retaliation or discrimination claim.

But Justice Ruth Bader Ginsburg was blunt.

"Did Davis ever have that authority, because the record as far as we have it says that the work assignment, what Vance was doing, came from the chef or from [general manger], and the most that Davis did was transmit the chef's orders of where people would be stationed."

The Obama administration supports neither side, but Justice Department attorney Sri Srinivasan argued that a person qualifies as a supervisor when he or she controls a subordinate's work activities and subjects that person to harassment.

"The ability to carry out the harassment is implicated in that the victim will lack the same ability to resist the harassment or to report it," Srinivasan said.

Justice Elena Kagan raised a hypothetical of a professor who subjects his secretary to a "complete hostile work environment on the basis of sex," but has no ability to hire or fire her.

"It's actually more difficult for the secretary to complain about the professor than it would be for the secretary to complain about the head of secretarial services" who hired her. Kagan said under the legal standard adopted by the appeals court in the Vance case, that professor would also not be considered supervisor even if he evaluates the secretary's work performance every year.

Justice Stephen Breyer suggested the more flexible legal standard adopted by the EEOC and three other appeals courts would be the way to go.

"Apparently, for about a dozen years, the EEOC has as an alternative basis for qualifying as a supervisor, that individual has authority to direct the employee's daily work activities."

The court has options for dealing with the Vance case and a decision is not expected before spring.

Several justices suggested throwing the case back to the lower courts to develop more fully who actually had a supervisory role at the Indiana university's food services division. Others were wary of adopting a broad binding rule, when such workplace disputes are all fact-specific and often do not follow traditional worker-employer roles.

The National Federation of Independent Business and the U.S. Chamber of Commerce are supporting the university. They suggest the changing economy will put companies at risk when determining managerial duties.

"This is consistent with workplaces across America today, where jobs are less hierarchical, more collaborative, and so where you have got more senior employees by virtue of their experience or job title, just a paper title, are in a broad sense team leaders of the like in the workplace," said Gregory Garre, representing the university. "That doesn't mean they are supervisors in any traditional sense."

The AARP and National Partnership for Women & Families are backing Vance. Those groups worry restricting who qualifies as a supervisor would allow business to give hiring and firing power to as few people as possible, to limit liability. They said that would leave the law "toothless."